This paper proposes a reinforced soft gripper with a mechanically strengthened electroadhesion pad and a multi-layered dielectric elastomer actuator, for a practical robotic application. The mechanical reinforcement of the electroadhesion pad is achieved by a metallic electrode pattern printed on flexible polyimide film, which has a higher elastic modulus than typical soft materials. To maximize the performance of the proposed electroadhesion pad, we analyze the electroadhesion force in aspects of the thickness of the insulation layer. Moreover, the multi-layered dielectric elastomer actuator is used to increase the bending force of the soft finger. With this study, we demonstrate dynamic picking and placing tasks with the proposed gripper assembled in a robotic system. The gripper can lift and move objects of various shapes weighing up to 625 g, while the gripper's mass is 6.2 g.